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23 April 2024 |
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Quasiclassical and Quantum Systems of Angular Momentum. Part I. Group Algebras as a Framework for Quantum-Mechanical Models with Symmetries | | J. J. Sławianowski
; V. Kovalchuk
; A. Martens
; B. Gołubowska
; E. E. Rożko
; | | Date: |
23 Jul 2010 | | Abstract: | We use the mathematical structure of group algebras and $H^{+}$-algebras for
describing certain problems concerning the quantum dynamics of systems of
angular momenta, including also the spin systems. The underlying groups are
${
m SU}(2)$ and its quotient ${
m SO}(3,mathbb{R})$. The scheme developed
is applied in two different contexts. Firstly, the purely group-algebraic
framework is applied to the system of angular momenta of arbitrary origin,
e.g., orbital angular momenta of electrons and nucleons, systems of quantized
angular momenta of rotating extended objects like molecules. The other
promising area of applications is Schr"odinger quantum mechanics of rigid body
with its often rather unexpected and very interesting features. Even within
this Schr"odinger framework the algebras of operators related to group
algebras are a very useful tool. We investigate some problems of composed
systems and the quasiclassical limit obtained as the asymptotics of "large"
quantum numbers, i.e., "quickly oscillating" functions on groups. They are
related in an interesting way to geometry of the coadjoint orbits of ${
m
SU}(2)$. | | Source: | arXiv, 1007.4121 | | Services: | Forum | Review | PDF | Favorites | |
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